"Well, I haven't heard many people say that and I don't think many people think that's true. I think I'm in pretty good shape with my Republican colleagues. They've elected me three times to my position, the last two times without any opposition, really."

For Alexander, a former Tennessee governor and two-time presidential candidate whose checkered shirts and pickup truck on the campaign trail failed to gain him the White House, his exit from the Senate GOP's leadership was more about gaining freedom, he said.

He wants to work across the aisle with Democrats on problems that need solving, he said. That's necessary because it takes 60 votes to accomplish anything in the Senate. There are currently 51 Democrats and two independents who caucus with them and 47 Republicans.

Now out of the leadership, he'll have more running room to help reach interparty agreements than he would ever have inside the leadership.

"The rarest privilege of being a senator is your autonomy. You're one of a hundred in an organization that operates by unanimous consent. You're free to do whatever you want to do. And when you go to the leadership table, you exchange some of your independence for a seat at the leadership table. I'm giving that up to get my independence back."

An example of where greater independence might have come in handy, Alexander said, was on a project like the so-called Gang of Six. That bipartisan group of senators developed a framework to reduce deficits and debt. It was eventually overtaken, however, by events, including the creation of the congressional supercommittee.

Echoing the Republicans on the gang, and perhaps demonstrating why being in the leadership might have had its challenges for him, Alexander expressed a view, generally heretical in congressional Republican circles, that he was open to more revenue (that is, collecting more taxes) under one, significant condition: that entitlement reform be a part of any such package.

My own position is the debt is such a big problem that if we're going to get a $4 trillion reduction over the next ten years and even more after that. I'm willing to consider a number of steps, including revenue increases, but only if we deal with the entitlement problem.

Another project he'll have more latitude to work on is a bipartisan effort with Sen. Dianne Feinstein (D-CA) and Sen. Lisa Murkowski (R-AK) to find a place to store nuclear waste. Tennessee has the nuclear plants that are part of the Tennessee Valley Authority as well as the Oak Ridge National Laboratory which conducts nuclear research.